1. Field of the Invention
The present invention relates to a method for reconstructing the shape and position of objects in three-dimensional space from at least two projections of said objects obtained by transmission of waves influenced by their passage through said objects from sources of said waves.
The term "object" is understood to mean a continuous ensemble which may or may not be a massive structure and which has essentially constant and homogenous physical characteristics such as, for example, blood vessels or bones in medical imaging or veins in geological formations.
The invention is also directed to a device for carrying out the method aforesaid.
2. Description of the Prior Art
The usual methods of locating an object in space are based on observation, from a number of different positions, of the external contours of the object to be defined and located.
The most common examples are directly derived from human stereoscopic vision. A similar approach is found in other fields such as geophysics or medicine irrespective of the waves employed, which range from electromagnetic radiation (x-rays, radar, standard vision) to sound waves (sonar, ultrasonic scanning). All these methods employ in all cases the abrupt differences of images (in attenuation or in reflection) for locating the contours of the object.
In order to locate an object with precision, these different methods make it necessary to surround the object with a sufficient number of observation points in order to define its contour. In the case of complex or irregular objects, this number can become very large, and the observation points must sometimes be so arranged as to surround the object completely, as in the case of a scanner, for example.
In the case of observations of "translucent" objects, in which the waves penetrate into the object without being totally absorbed, as in the case of x-ray images, an additional item of information appears in regard to the thickness of the object traversed. The attenuation is in fact a function of the coefficient of attenuation of the material traversed as well as the thickness of said material.
As indicated in the foregoing, the same situation occurs in the transmission of pressure waves such as seismic waves, for example. However, it is also possible in such a case to utilize the transit time aspects which also depend on the nature and thickness of the media being traversed.
In all cases, there therefore appears a relationship between the phenomenon observed and the distance traversed within the object.
If an object is subjected to waves which pass through it, and if the received waves are imaged, it is possible to obtain a map of the amplitude variation of said waves as a function, in particular, of the distance traversed by a ray within the object.
A well-known image of a map of this type is a radiograph. The lighter a point is on such a map, for example, the greater is the distance traversed by a ray within the object.
Any illuminating system in which there exists for each source only one ray which is clearly defined by its origin and its point of intersection with a known position on a photograph, and which passes through a point in space, will make it possible to establish a map of the modulation of the illuminating beam as a function of the distances traversed within the object.
Different types of projection naturally come to mind:
projections with parallel rays when the source is at infinity and when the receivers cover a reception plane,
conical projections when the source is at a finite distance,
more complex projections when the sources and the receivers are located on straight lines which are neither secant nor parallel, or else any other combination which makes it possible to "cover" a portion of space.
The most usual example of a conical projection is a radiographic image, or radiograph.
A single radiograph does not make it possible to reconstruct the spatial position of a given object although this radiograph offers much more information to its observer than a "photographic" image, in particular on the internal structure of the object in question.
Should it be desired to obtain more information on the interior of the object, it then becomes necessary to make a number of radiographs in accordance with a practice well known to radiologists. Sometimes, two radiographic images are not sufficient even for relatively simple objects, and it proves necessary in such cases to obtain a greater number from specific points.
Thus, in the case of a scanner, the entire circumference of an object is scanned. This involves making a very large number of projections of the object in order to reconstruct its shape and its position in space.
However, a scanner is an extremely complex and costly apparatus.
Attempts have been made to reconstruct an object from two projections (see Computer Vision, Graphics and Image Processing No. 3, Sept. 1984, A. Kuba). However, this method is applicable only to a limited number of cases.